(X^2+7x+10)/2=44

Solution for (X^2+7x+10)/2=44 equation:

(X^2+7X+10)/2=44

We move all terms to the left:

(X^2+7X+10)/2-(44)=0

We multiply all the terms by the denominator


(X^2+7X+10)-44*2=0

We add all the numbers together, and all the variables

(X^2+7X+10)-88=0

We get rid of parentheses

X^2+7X+10-88=0

We add all the numbers together, and all the variables

X^2+7X-78=0

a = 1; b = 7; c = -78;
Δ = b2-4ac
Δ = 72-4·1·(-78)
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-19}{2*1}=\frac{-26}{2}
=-13
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+19}{2*1}=\frac{12}{2}
=6
$